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The International Baccalaureate and the Transition to STEM Higher Education

Perspectives from an admissions tutor Chris Sangwin

School of Mathematics University of Birmingham

July 2013

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 1 / 17

UoB current offer

A-level BSc: A(maths)+AB MSci: A*(maths)+AA or AAA to include maths & further mathematics. BSc programmes: IB35 with HL Maths 6 MSci programmes: IB36 with HL Maths 7 IB36 with HL Maths 6 and HL Further Maths 6

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 2 / 17

UoB current offer

A-level BSc: A(maths)+AB MSci: A*(maths)+AA or AAA to include maths & further mathematics. BSc programmes: IB35 with HL Maths 6 MSci programmes: IB36 with HL Maths 7 IB36 with HL Maths 6 and HL Further Maths 6

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 2 / 17

G100 entry 2014 to Russell Group

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 3 / 17

Summary: Russell Group

All require HL 6 or better. Overall scores 33 1 34 3 35 5 36 4 37 2 38 1 39 3 Could see no reference to SL Further Mathematics.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 4 / 17

Summary: Russell Group

All require HL 6 or better. Overall scores 33 1 34 3 35 5 36 4 37 2 38 1 39 3 Could see no reference to SL Further Mathematics.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 4 / 17

Entry to Birmingham

Approx 900 applicants, cohort about 170. 2012 8 applicants, 4 rejected, 3 declined, 1 insurance. Entry: 0. 2013 13 applicant, 1 rejected, 8 declined, 4 insurances.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 5 / 17

Entry to Birmingham

Approx 900 applicants, cohort about 170. 2012 8 applicants, 4 rejected, 3 declined, 1 insurance. Entry: 0. 2013 13 applicant, 1 rejected, 8 declined, 4 insurances.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 5 / 17

Entry to Birmingham

Approx 900 applicants, cohort about 170. 2012 8 applicants, 4 rejected, 3 declined, 1 insurance. Entry: 0. 2013 13 applicant, 1 rejected, 8 declined, 4 insurances.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 5 / 17

Comparisons are very difficult

Exam papers and mark schemes are very difficult to get. (see http://www.freeexampapers.com/)

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 6 / 17

Expert Group Report, 2006. The study hours

The study hours for the IB Higher Level were recommended to be 240 – opinion differed as to whether or not this was generally achieved in practice – and for A level around 250-300 hours. It was expected, therefore, that the A level specification would contain more material than the IB Higher Level but this was found to be not the case.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 7 / 17

Content

International Baccalaureate Induction Complex numbers Matrices Kinematic problems GCE A level Mathematics Odd, even and periodic functions Polynomial inequalities Small angle approximations Coordinate geometry of circle Recurrence relationships Parametric equations of curves General solution of trigonometric equations Trapezium and Simpson’s rules

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 8 / 17

It was agreed that the major topics unique to the IB Higher Level needed introduction, assimilation and application, and practice whereas the topics unique to the A level were essentially additional applications of what had been already taught. Taking into account the time needed to cover these unique items the group suggested that the IB Higher Level content specification was between 10 and 20% larger than that of the A level.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 9 / 17

Assessments

The IB objectives appear to be more modest than those of A level but detailed examination of the papers suggested that all the IB objectives are tested and some of the A level objectives seem to be over ambitious.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 10 / 17

Entrance to R.M.A Woolwich 1880

Apply the second law of motion to prove that the path of a projectile in vacuo is a parabola. If balls be fired at the same instant from two cannons with equal velocities at angles of elevation, α and β respectively, so that both hit the same mark, and t′ the time between their returning to the horizontal plane through the point of projection, prove that t′ = 2t cos2 α + β 2

• .

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 11 / 17

Entrance to R.M.A Woolwich 1880

Apply the second law of motion to prove that the path of a projectile in vacuo is a parabola. If balls be fired at the same instant from two cannons with equal velocities at angles of elevation, α and β respectively, so that both hit the same mark, and t′ the time between their returning to the horizontal plane through the point of projection, prove that t′ = 2t cos2 α + β 2

• .

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 11 / 17

Entrance to R.M.A Woolwich 1880

Apply the second law of motion to prove that the path of a projectile in vacuo is a parabola. If balls be fired at the same instant from two cannons with equal velocities at angles of elevation, α and β respectively, so that both hit the same mark, and t′ the time between their returning to the horizontal plane through the point of projection, prove that t′ = 2t cos2 α + β 2

• .

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 11 / 17

June 1971 “Mathematics"

A projectile is fired with an initial velocity of magnitude V inclined at an angle α above the horizontal. Find the equation of the trajectory referred to the horizontal and vertical axes through the point of projection. A projectile is fired horizontally from a point O, which is at the top of a cliff, so as to hit a fixed target in the water, and it is observed that the time of flight is T. It is found that, with the same initial speed, the target can also be hit by firing at an angle α above the horizontal. Show that the distance of the target from the point at sea-level vertically below O is 1

2gT 2 tan α.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 12 / 17

June 2003, “Mechanics 1".

Air resistance should be neglected in this question. A bottle of champagne is held with its cork 1.5m above a level floor. The cork leaves the bottle at 60o to the horizontal. The cork has vertical component of velocity of 9ms−1, as shown in Fig. 4.

• Fig. 4.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 13 / 17

1

Show that the initial horizontal component of velocity is 5.20ms−1, correct to three significant figures. [2]

2

Find the maximum height above the floor reached by the cork. [3]

3

Write down an expression in terms of t for the height of the cork above the floor t seconds after projection. [2] After projection, the cork is in the air for T seconds before it hits the floor.

4

Show that T satisfies the equation 49T 2 − 90T − 15 = 0. Hence show that the cork is in the air for 1.99s, correct to three significant figures. Calculate the horizontal distance travelled by the cork before it hits the floor. [5]

5

Calculate the speed with which the cork hits the floor. [3]

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 14 / 17

Grade comparisons

Instead, it was agreed that the A Level A/B borderline is lower than the IB Higher Level 7/6 borderline (the top of IB level 6 is equivalent to A level grade A). It was agreed that the A/B boundary was not as low as the IB Higher Level 6/5 boundary.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 15 / 17

UCAS tariff

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 16 / 17

Conclusion

Birmingham IB offer is in line with Russell Group mathematics. IB offers unfairly high compared to A-level.

Chris Sangwin (University of Birmingham) IB and HE STEM July 2013 17 / 17